We have the following system:
Here, a simple solution to find the answer is to graph the two lines and see how many times they intersect.
I've attached a graph, with in red and the other equation in blue.
See that the lines only intersect once, at . This means the system only has one solution.
You change the equation into "graphable" equations
y<-4/5x+4
y>1/2x-3
Angular acceleration is change of angular velocity over time:
α = 5 / 8 = 0.625 rev / s²
Number of revolutions of the 1st part:
α · t² /2 = 0.625 * 8² / 2 = 20 rev.
The 2nd part:
α = 5/12 = 0.41667 rev/s²
5 * 12 - ( 0.41667 * 12² / 2 ) = 60 - 30 = 30 rev.
In total: 20 + 30 = 50 revolutions